Astronomy & Astrophysics

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Issue		A&A Volume 435, Number 3, June I 2005
Page(s)		901 - 925
Section		Interstellar and circumstellar matter
DOI		10.1051/0004-6361:20042381

A&A 435, 901-925 (2005)
DOI: 10.1051/0004-6361:20042381

A detailed study of the rotating toroids in G31.41+0.31 and G24.78+0.08

M. T. Beltrán¹, R. Cesaroni¹, R. Neri², C. Codella³, R. S. Furuya⁴, L. Testi¹ and L. Olmi³

¹ INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
e-mail: mbeltran@arcetri.astro.it
² IRAM, 300 rue de la Piscine, 38406 Saint Martin d'Hères, France
³ Istituto di Radioastronomia, INAF, Sezione di Firenze, Largo E. Fermi 5, 50125 Firenze, Italy
⁴ Division of Physics, Mathematics, and Astronomy, California Institute of Technology, MS 105-24, Pasadena, CA 91125, USA

(Received 17 November 2004 / Accepted 27 January 2005 )

Abstract
We present the results of high angular resolution millimeter observations of gas and dust toward G31.41+0.31 and G24.78+0.08, two high-mass star forming regions where four rotating massive toroids have been previously detected. The CH₃CN (12-11) emission of the toroids in G31.41+0.31 and core A1 in G24.78+0.08 has been modeled assuming that it arises from a disk-like structure seen edge-on, with a radial velocity field. For G31.41+0.31 the model properly fits the data for a velocity $v_{\rm rot}\simeq 1.7$ km s^-1 at the outer radius $R_{\rm out}\simeq 13400$ AU and an inner radius $R_{\rm inn}\simeq 1340$ AU, while for core A1 in G24.78+0.08 the best fit is obtained for $v_{\rm rot}\simeq 2.0$ km s^-1 at $R_{\rm out}\simeq 7700$ AU and $R_{\rm inn}\simeq 2300$ AU. Unlike the rotating disks detected around less luminous stars, these toroids are not undergoing Keplerian rotation. From the modeling itself, however, it is not possible to distinguish between constant rotation or constant angular velocity, since both velocity fields suitably fit the data. The best fit models have been computed adopting a temperature gradient of the type $T \propto R^$ , with a temperature at the outer radius $T_{\rm out}\simeq 100$ K for both cores. The $M_{\rm dyn}$ needed for equilibrium derived from the models is much smaller than the mass of the cores, suggesting that such toroids are unstable and undergoing gravitational collapse. The collapse is also supported by the CH₃¹³CN or CH₃CN line width measured in the cores, which increases toward the center of the toroids. The estimates of $v_{\rm inf}$ and $\dot M_{\rm acc}$ are ~2 km s^-1 and $\sim$ $3\times10^~M_\odot$ yr^-1 for G31.41+0.31, and ~1.2 km s^-1 and $\sim$ $9\times10^~M_\odot$ yr^-1 for G24.78+0.08 A1. Such large accretion rates could weaken the effect of stellar winds and radiation pressure and allow further accretion on the star. The values of $T_{\rm rot}$ and $N_{\rm CH_3CN}$ , derived by means of the RD method, for both G31.41+0.31 and the sum of cores A1 and A2 (core A of Codella et al. 1997, A&A, 325, 282) in G24.78+0.08 are in the range 132-164 K and 2- $8\times10^$ cm^-2. For G31.41+0.31, the most plausible explanation for the apparent toroidal morphology seen in the lower K transitions of CH₃CN (12-11) is self-absorption, which is caused by the high optical depth and temperature gradient in the core.

Key words: ISM: individual: G31.41+0.31, G24.78+0.08 -- ISM: molecules -- radio lines: ISM -- stars: formation

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